Extensions and improvements of Sherman's and related inequalities for n-convex functions

被引：5
|
作者：
Bradanovic, Slavica Ivelic [1 ]
Pecaric, Josip [2 ]
机构：
[1] Univ Split, Fac Civil Engn Architecture & Geodesy, Matice Hrvatske 15, Split 21000, Croatia
[2] Univ Zagreb, Fac Text Technol, Prilaz Baruna Filipovica 30, Zagreb 10000, Croatia
来源：
OPEN MATHEMATICS | 2017年 / 15卷
关键词：
Sherman inequality; Majorization inequality; Jensen inequality; n-convex; Green functions; Fink identity; Cebysev functional; Means; BOUNDS;
D O I：
10.1515/math-2017-0077
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper gives extensions and improvements of Sherman's inequality for n-convex functions obtained by using new identities which involve Green's functions and Fink's identity. Moreover, extensions and improvements of Majorization inequality as well as Jensen's inequality are obtained as direct consequences. New inequalities between geometric, logarithmic and arithmetic means are also established.
引用
收藏
页码：936 / 947
页数：12
相关论文
共 50 条
  • [21] LINEAR OPERATORS INEQUALITY FOR n-CONVEX FUNCTIONS AT A POINT
    Pecaric, Josip
    Praljak, Marjan
    Witkowski, Alfred
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2015, 18 (04): : 1201 - 1217
  • [22] MEANS INVOLVING LINEAR FUNCTIONALS AND n-CONVEX FUNCTIONS
    Jaksetic, J.
    Pecaric, J.
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2011, 14 (03): : 657 - 675
  • [23] Weighted averages of n-convex functions via extension of Montgomery’s identity
    Asif R. Khan
    Josip E. Pečarić
    Marjan Praljak
    Arabian Journal of Mathematics, 2020, 9 : 381 - 392
  • [24] Extensions of Fejcr type inequalities for GA-convex functions and related results
    Latif, Muhammad Amer
    FILOMAT, 2023, 37 (24) : 8041 - 8055
  • [25] Weighted majorization inequalities for n-convex functions via extension of Montgomery identity using Green function
    Aglić Aljinović A.
    Khan A.R.
    Pečarić J.E.
    Arabian Journal of Mathematics, 2018, 7 (2) : 77 - 90
  • [26] On convex functions and related inequalities
    Vaziri, Parvaneh
    Khodabakhshian, Hadi
    Safshekan, Rahim
    ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2023, 50 (01): : 91 - 98
  • [27] On ψ-convex functions and related inequalities
    Aydi, Hassen
    Samet, Bessem
    De la Sen, Manuel
    AIMS MATHEMATICS, 2024, 9 (05): : 11139 - 11155
  • [28] BOUNDS ON THE DERIVATIVES OF A FUNCTION VIA THE THEORY OF N-CONVEX FUNCTIONS
    FARWIG, R
    ZWICK, D
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1986, 118 (01) : 97 - 106
  • [29] APPROXIMATION IN LP[0,1] BY N-CONVEX FUNCTIONS
    SWETITS, JJ
    WEINSTEIN, SE
    XU, YS
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1990, 11 (1-2) : 167 - 179
  • [30] Some Improvements on Hermite-Hadamard's Inequalities for s-convex Functions
    Li, Yujiao
    Du, Tingsong
    JOURNAL OF MATHEMATICAL STUDY, 2016, 49 (01): : 82 - 92
12345